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Popular >

e^x= k/((x-3))

Solution

e^{x} = \frac{k}{( x - 3 )}

Solution

x = W (\frac{k}{e ^{3}}) + 3

Solution steps

e^{x} = \frac{k}{( x - 3 )}

Prepare

e^{x} = \frac{k}{( x - 3 )}

for Lambert form:

e^{x} (x - 3) = k

Rewrite the equation with

x - 3 = u

and

x = u + 3

e^{(u + 3)} ((u + 3) - 3) = k

Simplify

e^{u + 3} u = k

Rewrite

e^{u + 3} u = k

in Lambert form:

e^{u} u = \frac{k}{e ^{3}}

Solve

e^{u} u = \frac{k}{e ^{3}} : u = W (\frac{k}{e ^{3}})

u = W (\frac{k}{e ^{3}})

Substitute back

u = x - 3,

solve for

x

Solve

x - 3 = W (\frac{k}{e ^{3}}) : x = W (\frac{k}{e ^{3}}) + 3

x = W (\frac{k}{e ^{3}}) + 3

Verify Solutions:

x = W (\frac{k}{e ^{3}}) + 3

True

The solution is

x = W (\frac{k}{e ^{3}}) + 3

Verify Solutions:

x = W (\frac{k}{e ^{3}}) + 3

True

The solution is

x = W (\frac{k}{e ^{3}}) + 3

Popular Examples

1 = 10 \cdot 0.7 5^{x}

0=12000(0.85)^{n-1}

0 = 12000 (0.85)^{n - 1}

4^{n} = 1024

322 = 2^{n}

3^{4x+3}=8^{-x+2}

3^{4 x + 3} = 8^{- x + 2}

Frequently Asked Questions (FAQ)

What is the answer to e^x= k/((x-3)) ?
The answer to e^x= k/((x-3)) is x=\W(k/(e^3))+3